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Gradation of the Severity of Sepsis

Learning in a Causal Probabilistic Network

Ward, Logan Morgan

DOI (link to publication from Publisher):10.5278/VBN.PHD.MED.00064

Publication date:2016

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GRADATION OF THE SEVERITY OF SEPSIS

LEARNING IN A CAUSAL PROBABILISTIC NETWORK

BYLOGAN WARD

DISSERTATION SUBMITTED 2016

GRADATION OF THE SEVERITY OF

SEPSIS

LEARNING IN A CAUSAL PROBABILISTIC NETWORK

by

Logan Ward

Dissertation submitted 2016

Thesis submitted: June 28, 2016

PhD supervisor: Professor Steen Andreassen,

Aalborg University

PhD committee: Professor Yuval Shahar, Ben-Gurion University of the Negev

Associate Professor Vittorio Sambri,

University of Bologna

Professor Johannes Struijk, Aalborg

University

PhD Series: Faculty of Medicine, Aalborg University

ISSN (online) – 2246-1302ISBN (online) - 978-87-7112-767-6

Published by:

Aalborg University Press

Skjernvej 4A, 2nd floor

DK – 9220 Aalborg Ø

Phone: +45 99407140

[email protected]

forlag.aau.dk

© Copyright: Logan Morgan Ward

Printed in Denmark by Rosendahls, 2016

I

CV

Personal Information

Logan Morgan Ward

Born December 20, 1988, Lower Hutt, New Zealand.

Academic Profile and Research Experience

Logan received his BE (1st Class Honours) in Mechanical Engineering from

University of Canterbury, New Zealand in 2010. Following a brief tenure as a

research engineer at Industrial Research Limited (a New Zealand Crown Research

Institute), he moved to Denmark to pursue his M.Sc. in Biomedical Engineering and

Informatics, with the degree awarded by Aalborg University in 2012. He began his

PhD studies at Aalborg University’s Department of Health Science and Technology

in September 2012. During the PhD study, Logan had contributions accepted at five

international conferences, with the results of his research producing four papers (two

published, one invited and under review, one submitted) and a patent application.

III

ENGLISH SUMMARY

Sepsis is a severe response to infection, characterised by systemic inflammation

leading to tissue damage and organ dysfunction. In septic patients, early, appropriate

antibiotic treatment is vital, more so in patients with severe sepsis.

The aim of this PhD project was to further develop an existing causal probabilistic

network (CPN) model of sepsis through learning: both manually through evidence-

based adjustments to the model and automatically through machine learning from

patient databases. The model forms part of a larger CPN used by the decision support

system Treat, which provides advice for optimal antibiotic treatment.

The results of the project were described in four papers. Paper I described the manual

learning process where continuous distributions were introduced for infection

variables. Paper I showed that manual learning is an effective, albeit limited, method

of constructing a CPN. On a small validation dataset, the manually learned CPN

presented a non-significant improvement in prediction of patients with bacteraemia

compared to the previous model. Papers II and III described the automatic learning

process wherein the model was tuned to function as a standalone predictor of 30-day

mortality. The tuned model was significantly better than both the previous model and

other scoring systems described in the literature. Paper IV presented an application

of the standalone model tuned to predict bacteraemia. It showed that risk-based

stratification of patients suspected of sepsis could be used to improve the cost-

effectiveness of rapid diagnostics, e.g. polymerase chain reaction, which would

otherwise be too expensive to use for all patients.

The resulting models for the prediction of bacteraemia and 30-day mortality can be

used as standalone systems or reintegrated with the Treat decision support system.

As a standalone model, the output can be considered as an intelligent biomarker for

sepsis, tuned from real patient data. Future work involves the development of a more

complete picture of the inflammatory response, including the time-course, which

could enable earlier detection of infection or treatment revision in patients for whom

infections are not microbiologically documented.

V

DANSK RESUME

Sepsis er kroppens respons til alvorlig infektion, kendetegnet ved systemiske

inflammation som fører til vævsbeskadigelse og organ dysfunktion. I septiske

patienter er tidlig, dækkende antibiotika behandling afgørende, desto mere i patienter

med svær sepsis.

Formålet af dette PhD projekt var at videreudvikle en existerende kausalt

probabilistisk netværk (engelsk: Causal Probabilistic Network, eller CPN) model for

sepsis igennem læring: både manual læring igennem evidens-baserede justeringer af

modellen og automatisk læring igennem maskin-læring fra patientdatabaser.

Modellen er en del af et større CPN inkluderet i beslutningsstøttesystemet Treat, som

giver råd om optimal antibiotika behandling.

Projektets resultater blev beskrevet i fire artikler. Artikel I beskrev den manuelle

læringsproces, hvor kontinuerte fordelinger blev introduceret for infektionsvariabler.

For et mindre valideringsdatasæt, viste CPN’et baseret på manuel læring ikke

signifikant forbedring i forudsigelse af patienter med bakteræmi sammenlignet med

den tidligere model. Artikel II og III beskrev den automatiske læringsproces, hvori

modellen blev tunet til at fungere som en enestående prædiktor af 30-dages mortalitet.

Den tunede model var signifikant bedre end både den forrige model og andre

scoringsystemer beskrevet i literaturen. Artikel IV viste en anvendelse af den

selvstændige model tunet til at forudsige bakteræmi. Den viste at risiko-baseret

stratificering af patienter mistænkt for sepsis kunne bruges til at øge cost-

effectiveness af hurtig diagnostiske metoder, f.eks polymerase chain reaction, som

ville ellers være for dyr til at bruge på alle patienter.

De resulterende modeller for forudsigelse af bakteræmi og 30-dages mortalitet kan

bruges som selvstændige systemer eller kan integreres med beslutningsstøttesystemet

Treat. Anvendt som selvstændigt system, kan outputtet betragtes som en intelligent

biomarkør for sepsis, tunet fra rigtige patientdata. Fremtidigt arbejde involverer

udvikling af et mere komplet billede af den inflammatorikse respons, inklusiv

tidsforløbet, som kunne give mulighed for tidligere detektion af infektion eller

revidering af behandling af patienter, hvis infektioner ikke er mikrobiologisk

dokumenteret.

VII

ACKNOWLEDGEMENTS

I have learned a lot during my time as a PhD student at Aalborg University, and the

experience has certainly helped me grow both professionally and personally. A new

language, a new culture and limitless opportunity to travel was all part and parcel.

The academic- and life-lessons learned stand me in good stead for whatever comes

next.

First, I would like to thank my PhD supervisor, Steen Andreassen, for his ongoing

support and optimism, and continuing belief that a breakthrough was just around the

corner.

I would like to thank Professors Mical Paul and Leonard Leibovici from Tel Aviv

University, Israel for their insights as co-authors, and for provision of the data which

made the PhD project possible.

Thank you to everyone at Treat Systems for their help with accessing data and the

models provided.

I would like to express my gratitude to my colleagues at AAU, in particular those at

MMDS. Thank you for all the support, good cheer and company.

Thank you to all those who “forced” me to speak Danish – through making my life

difficult you have made it so much easier.

Thank you to all my friends and family for their support and always believing in me.

Last but certainly not least I would like to thank Vladina, for keeping me on track

and focused on the end goal, and more importantly, keeping me sane.

IX

TABLE OF CONTENTS

Chapter 1. Introduction .......................................................................................... 11

Chapter 2. Background .......................................................................................... 17

2.1. CPN Modelling ............................................................................................. 17

2.2. Learning in CPNs .......................................................................................... 20

2.2.1. Manual Learning .................................................................................... 20

2.2.2. Machine Learning .................................................................................. 20

2.3. The Treat Model of Infection ........................................................................ 21

2.4. Sepsis: The Modeller’s Perspective .............................................................. 23

2.4.1. What Happens to a Patient During Sepsis .............................................. 23

2.4.2. Describing the Patient’s Condition......................................................... 26

Chapter 3. Manual Learning: Development of Continuous Distributions ......... 29

Chapter 4. Automatic Learning: Model Tuning to Improve Predictive

Performance ............................................................................................................ 33

Chapter 5. Applications of SepsisFinder ............................................................... 41

Chapter 6. Discussion ............................................................................................. 47

6.1. Main Findings ............................................................................................... 47

6.2. Future Work .................................................................................................. 49

Literature list ........................................................................................................... 51


X

LIST OF PAPERS

This thesis is based on a collection of papers, which will be referred to in the text by

their corresponding roman numerals:

Paper I: Ward, L., Mogensen, M.L., Paul, M., Leibovici, L and Andreassen,

S. (2014), A Bayesian Approach to Model-Development: Design of

Continuous Distributions for Infection Variables. 19th World Congress of the

International Federation of Automatic Control (IFAC) 24-29 August, 2014,

Cape Town, South Africa

Paper II: Ward, L., and Andreassen, S. (2015), A Bayesian Approach to

Model-Development: Automatic Learning for Tuning Predictive

Performance. 9th IFAC Symposium on Biological and Medical Systems, 31

August – 2 September, 2015, Berlin, Germany.

Paper III: Ward, L., Paul, M., Andreassen, S. Automatic Learning of

Mortality in a CPN model of the Systemic Inflammatory Response

Syndrome. (invited, under review: Mathematical Biosciences (Special

Issue))

Paper IV: Ward, L., Leibovici, L., Paul, M., and Andreassen, S. Risk-

assessment can improve cost-effectiveness of PCR testing of bacteremia

(Submitted)

11

CHAPTER 1. INTRODUCTION

Sepsis is a severe manifestation of a systemic infection and is associated with high

mortality rates: ranging from 15-60% (Angus et al. 2001, Martin et al. 2003, Vincent

et al. 2006). Early treatment with appropriate antimicrobials is vital: failure to initiate

early appropriate antimicrobial therapy increases mortality with an odds ratio of

approximately 2 (Paul et al. 2010). The decision support system Treat provides

advice on empirical antimicrobial therapy (before a pathogen is identified) and can

significantly increase the fraction of patients receiving appropriate antimicrobial

therapy (Kristensen et al. 1999, Paul et al. 2006b, Leibovici, Paul & Andreassen

2010, Kofoed et al. 2009), however there are additional clinical decisions during the

course of an infection that are not addressed by Treat. In chronological order from

the view of an infectious episode, these are: 1) early detection of the onset of

infection; 2) risk assessment to determine the diagnostic and treatment strategy; and

3) revision of therapy a few days after the initiation of therapy. This project focuses

on the risk assessment of patients suspected of infection.

Risk assessment of patients suspected of infection serves two purposes: to determine

the diagnostic strategy and to determine the aggressiveness of empirical therapy. In

each case, severity of illness is a driving factor. The current standard for sepsis

diagnosis is blood culture, which typically takes 2-4 days. In comparison, new rapid

molecular methods such as polymerase chain reaction (PCR) direct from blood are

much faster, identifying a pathogen in 6-12 hours (Liesenfeld et al. 2014,

Mwaigwisya, Assiri & O'Grady 2015). Molecular methods are however much more

expensive, and it is not currently feasible to order these tests for all patients suspected

of infection. A similar prioritisation exists when considering antimicrobial treatment:

although broad-spectrum antimicrobials may be able to eradicate most pathogens,

they have more undesirable side effects, have led to an increase in C. difficile

infections and widespread increase in resistance to antimicrobials (Vernaz et al. 2009,

Bartlett 2006, Laxminarayan et al. 2013). In each case, a mathematical risk

assessment allows for the balancing of costs and benefits.

Diagnosis and assessment of sepsis severity: SIRS

Traditionally, the relationship between infection and sepsis is understood to be as

depicted in Figure 1.1, where SIRS is the Systemic Inflammatory Response

Syndrome and bacteraemia refers to an infection in the blood-stream. SIRS is a non-

specific state of inflammation, defined at a 1992 consensus conference of the Society

of Critical Care Medicine and American College of Chest Physicians (Bone et al.

1992).


12

A patient has SIRS if they meet two or more of the following criteria:

Temperature >38°C or <36°C

White blood cell (WBC/leukocyte) count <4000 or >12000 cells/cm3

Heart rate > 90 bpm (tachycardia)

Respiratory rate > 20 breaths per minute

Sepsis is SIRS caused by an infection and non-infectious SIRS (NSIRS) refers to any

other aetiology such as trauma/surgery, burns or pancreatitis. Within SIRS and sepsis,

patients are also graded by severity, for example: severe sepsis is sepsis complicated

by organ dysfunction, and septic shock is severe sepsis with systolic blood pressure

less than 90 mmHg, refractory to fluid resuscitation.

Figure 1.1: The relationship between infection, sepsis and SIRS. Other blood-borne infections refer to all of those not caused by bacteria. Diagram adapted from (Bone et al. 1992)

The idea of SIRS is still part of the most commonly used definition of sepsis, however

it has been criticised by leading sepsis researchers – it is unspecific and overall not

very useful (Vincent 1997). In reality, almost all patients with an infection have some

degree of sepsis: they all have some degree of systemic involvement from the

immune system. Figure 1.2 proposes an alternate view where patients with an

infection instead fall into strata based the severity of their sepsis. The state of “no

sepsis” refers to those with minor infection, for example an infected cut on a finger.

The proposed states of sepsis severity are somewhat analogous to sepsis, severe

sepsis and septic shock; the new names allow some departure from the literature

definitions.

The continuous severity spectrum described in Figure 1.2 is that used in the Treat

decision support system. At its core, Treat is a stochastic model of the interaction of


13

Figure 1.2: An alternative view: almost all patients with an infection have some degree of sepsis and can be stratified by severity

bacteria, antimicrobials and the patient’s inflammatory response. This interaction is

modelled in a Causal Probabilistic Network (CPN). The part of the model which deals

with the inflammatory response is known as the Sepsis CPN. The Sepsis CPN is the

main contributor in evaluating the severity of illness. The Sepsis CPN’s performance

as a diagnostic or prognostic indicator can be evaluated by assessing its ability to

predict clinical outcomes such as positive blood culture (bacteraemia) and 30-day

mortality.

Several other methods for scoring sepsis or (general) illness severity are described in

the literature. The majority of clinical scores are based on logistic regression models.

These clinical scores tend to focus on information available at the bedside. Scores

used for sepsis patients include the modified rapid emergency medicine score

(mREMS) (Olsson, Terént & Lind 2004, Howell et al. 2007), the mortality in the

emergency department sepsis (MEDS) score (Shapiro et al. 2003), and the sequential

organ-failure assessment (SOFA) (Vincent et al. 1996).

Aim of the PhD study

The PhD study centres on the development of a family of models for the gradation of

the severity of sepsis. The starting point for the project is Treat’s Sepsis CPN, with

the goal of updating the Sepsis CPN and improving its performance in predicting

bacteraemia and 30-day mortality. The approach taken to solve the problem follows


14

a Bayesian philosophy: a stepwise updating of a priori understanding based on the

knowledge available. In this case domain knowledge is acquired from the literature,

opinions of clinical experts and from patient databases.

Figure 1.3 presents an overview of the PhD project in three stages. Chapter 2 presents

the background, including CPN technology and an overview of sepsis and its

manifestations, Chapters 3 and 4 present the manual and automatic learning stages of

model development, respectively, and Chapter 5 presents an application of the

learned SepsisFinder model: selection of high-risk patients for rapid diagnostic

testing. Chapter 6 then contains a discussion of key points and main findings of the

thesis, and suggestions for future work.

Figure 1.3: PhD Project Framework

The initial phase of the PhD project focused on building knowledge and

understanding of how sepsis develops and the typical markers, signs and symptoms

seen in patients. Literature concerned with the construction and performance of the

Treat CPN was also investigated. The Treat CPN serves as an example of a CPN

model that was constructed largely manually, that is, without applying machine

learning techniques. A search was also conducted into learning from data in medicine

and the machine learning methods available, notably expectation maximisation (EM)

learning. This research was important in building the domain knowledge required to

successfully construct a CPN and forms the background material presented in

Chapter 2.

The next phase of the project focused on model development, shown in the dashed

box in Figure 1.3. Stepwise improvement of the model via learning was conducted in


15

two stages: first by manual learning (Chapter 3) and then subsequently by automatic

learning (Chapter 4).

Chapter 3 summarises the work carried out in the manual learning stage: a set of

continuous distributions for infection variables that improve Treat’s prediction of

bacteraemia. The result of the manual learning was the Continuous (C-) Sepsis CPN.

This method of constructing CPNs was proven to be robust, and was the method used

in constructing the Treat CPN. This Chapter is based on Paper I.

Chapter 4 describes the automatic learning process and the results of tuning two

CPNs: one to predict 30-day mortality and one to predict bacteraemia in patients

suspected of sepsis. Applying machine learning gives the potential to use the

knowledge contained in patient databases, something that has not formally been done

in the Treat model. The result represents a significant improvement over the model

described in Paper I. This Chapter is based on Papers II and III which described two

Learned Sepsis CPNs, the L-Sepsis CPN (Paper II) and the LA-Sepsis CPN (Paper

III) that were tuned to predict 30-day mortality. Chapter 4 also describes the

SepsisFinder model, which was tuned to predict bacteraemia using a similar learning

strategy.

The third and final phase of the project is concerned with the application of the tuned

SepsisFinder model, and is described in Chapter 5. The SepsisFinder model is used

for risk-assessment, where the predicted probability of bacteraemia can be used to

define a group of high-risk patients for whom rapid diagnostic testing may be cost-

effective. Paper IV describes the use of SepsisFinder in assessing the cost-

effectiveness of one rapid diagnostic technique, PCR, in the emergency department.

This application was also described as part of a patent application (Application

number: PA 2015 00514) which centred on the idea that one parameter (sepsis

severity) can be used for many purposes, including but not limited to the prediction

of bacteraemia and 30-day mortality.

The main findings and scientific contribution of the thesis are discussed in Chapter

6. Suggestions for future work are also addressed, including the re-integration of the

Sepsis CPN within Treat, and the use of Sepsisfinder to describe the time-course of

infection. A full description of the time-course of infection would provide an

opportunity to address two of the remaining clinical problems not addressed by Treat:

early detection of the onset of infection and revision of therapy.

17

CHAPTER 2. BACKGROUND

This chapter provides the medical and technical background for the PhD project.

The type of mathematical model used in Sepsisfinder, a Causal Probabilistic Network

(CPN) is introduced. The basic principles of CPNs including how they are

constructed and used are explained. The medical problem-area, sepsis, is also

discussed from the modeller’s perspective, using the Treat CPN as an example. This

chapter represents the knowledge input to the modelling stage of the PhD project,

seen as the highlighted portion of Figure 2.1.

Figure 2.1 PhD project framework. This chapter describes the background (highlighted)

2.1. CPN MODELLING

CPNs, also referred to as Bayesian networks are a type of stochastic model. A CPN

can be represented graphically by a set of nodes, linked together by arrows as shown

in Figure 2.2. The arrows represent causal relationships between variables.

Numerically these arrows can be thought of as conditional probability tables. The

task of constructing a CPN consists of specifying the graphical structure and filling

out the associated conditional probability tables. Once constructed, the CPN updates

the probability distributions according to the axioms of probability theory based on

the entered evidence. CPNs are ideal for creating diagnostic models: inferences can

be made about unobservable variables based on available evidence, and when

accompanied by decision theory and utility functions they can also provide advice on

treatment selection.


18

Figure 2.2: Simple CPN model with one cause (Flu) and one effect (Fever). Two tables are shown: the top table specifies the a priori likelihood of Flu, and the bottom table is the conditional probability table for fever given flu. Adapted from (Andreassen 2000).

Figure 2.2 contains all the information required for probabilistic reasoning. For

example, it is possible to calculate the probability for Fever, P(Fever), as the sum of

the joint probabilities of Fever given Flu as in Equation 2.1:

P(Fever)=P(Fever|Flu=yes)P(Flu=yes)+P(Fever|Flu=no)P(Flu=no) (2.1)

Using Equation 2.1 we can calculate that P(Fever=yes) = 0.90*0.05 + 0.02*0.95 =

0.064 and P(Fever=no) = 0.10*0.05 + 0.98*0.95 = 0.936. Causal reasoning is simple

in this case as these probabilities are specified and can be read directly from the

conditional probability table. The ability to provide diagnostic reasoning, inferring

the likelihood of a cause based on the observation of an effect is perhaps less

apparent. Bayes’ Theorem provides the foundation for this type of reasoning; it

relates the conditional probability of event A given another event B to the conditional

probability of B given A. In this case A and B are Flu (the cause) and Fever (the

effect), as in Figure 2.2, and Bayes’ Theorem can be written as:

P(Flu|Fever)=P(Flu)P(Fever|Flu)

P(Fever) (2.2)

Equation 2.2 is vital to understanding how inference works in CPNs. In this simple

two variable case, we know the conditional probability P(Fever|Flu) and the a priori

probability of flu, P(Flu), and then observing Fever=yes, we can solve Bayes’

equation to infer the probability of Flu=yes, as in Equation 2.3. The factor

P(Fever|Flu)/P(Fever) in Equation 2.2 can be seen as the effect of the evidence: the

factor which the prior probability of Flu (P(Flu)) is multiplied by to give the posterior

probability.

P(Flu=yes|Fever=yes)=P(Flu=yes)P(Fever=yes|Flu=yes)

P(Fever=yes)=

0.05*0.90

0.064=0.703 (2.3)


19

The example shown in Figure 2.3 is another simple CPN, this time with two causes:

flu and throat infection, and two symptoms: fever and sore throat. Fever and sore

throat can each be caused by flu and/or throat infection, as indicated by the arrows.

The conditional probability tables are filled out when constructing the CPN,

specifying the joint probabilities for sore throat and fever respectively, given flu and

throat infection: P(Fever| Flu, Throat infection) and P(Sore throat | Flu, Throat

infection) (Figure 2.3, panel A). In this case, observing Fever=no and Sore

throat=yes allows us to infer that a throat infection is much more likely than the flu

(Figure 2.3, panel B).

Figure 2.3: Construction and use of a simple CPN. During construction (panel A), the structure and probability tables are specified using a top-down approach, following the flow of causality. During use (panel B), when the effects are observed, diagnostic reasoning can be applied, using the evidence to make inferences about the likely cause. Adapted from (Andreassen 2000).

The example in Figure 2.3 is simple enough that the inferred probabilities could be

calculated by hand. However, inference quickly becomes complicated as more nodes

and dependencies are added. For more complex CPNs, software solutions become

necessary. All CPNs used in this thesis were constructed using the commercial

software package Hugin (Hugin Expert A/S, Aalborg, Denmark), which was also

used to perform inference.


20

2.2. LEARNING IN CPNS

The construction of a CPN provides a unique opportunity for the fusion of data and

knowledge. Importantly, this knowledge may come from any one (or more) of a

number of sources: in the medical domain these could be patient databases, expert

opinion and reports in the scientific literature. Before beginning construction of a

model, it is important to understand the problem area: for the infectious process this

would include the pathogenesis and pathophysiology and what can be observed in a

patients, for example blood gases, haematology, vital signs etc. The model variables

and structure are then identified based on the knowledge acquired: this can be done

manually or automatically, the latter referring to the use of machine learning

techniques. During the construction of the CPN, the conditional probabilities may

themselves be considered stochastic variables; a priori distributions may be assigned,

and the result of learning is the set of a posteriori distributions.

2.2.1. MANUAL LEARNING

In the context of this thesis, manual learning refers to the specification of CPN

structure and conditional probability tables without applying machine learning

techniques. Manual learning therefore refers to all other forms of knowledge

acquisition; review and meta-analysis of the scientific literature, uni- or multivariate

analysis of patient data, or the transformation of expert opinion into explicit

conditional probabilities. Manual learning can be an effective method for

constructing CPNs: the Treat CPN, described in section 2.3 was constructed in this

way. Manual learning was also applied in the construction of the models described

in this thesis. The specific learning strategy used in described in Chapter 3 which is

based on Paper I.

2.2.2. MACHINE LEARNING

Machine learning from patient data can be used instead of or as a supplement to the

manual learning process used to construct a CPN. Traditionally, machine learning is

used to form classification models where cases must be assigned to one of two or

more groups based on a set of parameters (measurements/observations) which may

be continuous or categorical variables or regression models (prediction). If the

classification of each case is used as an input at the learning stage, the process is

termed “supervised” learning, whereas if the classification is not used as an input,

learning is “unsupervised”.

A range of machine learning algorithms exist, each with certain advantages and

disadvantages dependent on the type of problem. For this thesis, the discussion will

be limited to Expectation Maximisation (EM) learning (Lauritzen 1995), a maximum

likelihood method. An algorithm for EM learning is available in the Hugin software.


21

The learning process proceeds as follows. The CPN constructor specifies which

conditional probability tables should be learned: this may be any or all tables and/or

parts thereof. It is also possible to enforce zeros in conditional probability tables to

define impossibilities. Following the specification of what is to be learned, the EM

algorithm begins to iterate. The algorithm maximises the likelihood of all cases,

calculated as the product of the joint probability of the data for each case. In Hugin,

the algorithm terminates either when the specified maximum number of iterations is

reached or the tolerance for the difference in log-likelihood between two successive

iterations is reached.

If all of the nodes in a CPN are observed, and these observations are recorded in the

case data for learning, the learning process degenerates to counting and becomes

trivial. However, this is not the case for the sepsis model. The sepsis CPN contains

several latent (unobservable) variables which is an added difficulty where learning is

concerned. This is coupled with the fact that medical/clinical databases are typically

plagued by missing data; not every patient receives the same tests.

2.3. THE TREAT MODEL OF INFECTION

The Treat CPN was constructed via a semi-formal approach, using the literature,

expert opinion and patient data to specify the conditional probability tables. The

success of this technique has been demonstrated empirically through the success of

Treat (Kristensen et al. 1999, Paul et al. 2006b, Leibovici, Paul & Andreassen 2010,

Kofoed et al. 2009). The Treat CPN, shown in Figure 2.5, is very large, containing

approximately 6000 nodes. Within the CPN, eleven sites of infection are modelled,

each with local symptoms and findings and a set of relevant pathogens. One small

section of Treat describes the inflammatory response: the Sepsis CPN, highlighted in

Figure 2.5. Treat is specifically designed to account for geographical, demographical

and other hospital-specific differences in pathogen prevalence and resistance to

antimicrobials; it is calibrated to each specific hospital as part of the installation

process.

Treat’s advantage over clinicians is due to the ability of the CPN to hold knowledge

in the form of large arrays of conditional probability tables and to handle complex

probability calculus. The prescription of empirical antibiotic treatment involves a set

of decision points which the clinician must go through. First, the clinician must

decide whether the patient has an infection, and if so, where the infection is focused.

Based on the likely focus of infection, the clinician must then decide what the most

likely causative pathogen is. Given the most probable pathogen, which treatment

offers the best balance of coverage (dependent on local resistance patterns), potential

side-effects and cost? Empirical antimicrobial prescribing is not a trivial task, it

involves complex decision-making, and computerised decision support tools may be

able to improve the practice (Leibovici et al. 1999). The set of decisions made when


22

prescribing antimicrobials can be equated to the multiplication of large conditional

probability matrices, which is not a task that humans excel at.

Figure 2.5: The Treat CPN. The structure of the CPN is divided into 11 sites of infection, where the base units are pathogens. One small part of the network, the Sepsis CPN (highlighted), deals with the inflammatory response.

Treat has been described extensively in the literature, from the original concept

(Andreassen et al. 1999, Leibovici et al. 2000), through its development into a tool

suitable for research (Andreassen et al. 2005) to the results achieved through clinical

trials of the system (Paul et al. 2006b, Paul et al. 2006a, Paul et al. 2007, Leibovici

et al. 2007, Leibovici, Paul & Andreassen 2010). Treat was developed collaboratively

by researchers at Aalborg University (AAU) and Rabin Medical Centre, Israel as part


23

of an EU funded project (EU 5th framework, Information Society Technologies,

contract no.: IST-9999-11459) The stochastic model of infection shown in Figure 2.5

is combined with decision theory to provide advice that seeks to maximize the

probability of effective treatment while minimizing both the direct cost of the

treatment as well as the ecological cost of furthering antimicrobial resistance and any

side effects that may occur.

In an observational trial run in three major European hospitals, Treat showed great

improvements versus clinician-only regimes, improving covering antibiotic

treatment from 57% to 70% (Paul et al. 2006b). Treat also showed improvements

when used in a cluster-randomized interventional trial with appropriate empirical

antibiotic treatment in 73% of cases in interventional wards compared with 64% in

control wards (Paul et al. 2006b). Long-term (6 month) survival was also higher in

interventional wards, and even higher in cases where Treat’s recommendations were

followed (Leibovici, Kariv & Paul 2013).

2.4. SEPSIS: THE MODELLER’S PERSPECTIVE

This section uses Treat’s Sepsis CPN to explain sepsis from a modelling point of

view, describing its construction. To build a causal model, it is necessary to

understand the pathogenesis and pathophysiology of sepsis, and how this can be

recognised in terms of measureable variables such as clinical chemistry, blood gases,

haematology, etc. Section 2.4.1 describes what happens to a patient during sepsis in

terms of the physiological changes typically seen in sepsis patients. The variables

used by the Sepsis CPN and their links to sepsis pathophysiology are also described.

Section 2.4.2 describes how CPN models can be used to describe a patient’s

condition, defining the conditional probability tables linking the model parameters

and patient condition. This step can also be thought of as the development of a

composite biomarker.

2.4.1. WHAT HAPPENS TO A PATIENT DURING SEPSIS

The response to an infection depends on the severity of the disease, as well as other

host-specific factors: comorbidities and immune-status modifiers

(immunosuppressant drugs etc.). The SIRS criteria are present in most patients as

they are part of the general response to infection. Increasing severity of sepsis is

generally associated with a greater degree of organ dysfunction and/or failure. Figure

2.7 describes some of physiological alterations seen in sepsis: all major organ systems

are involved. Inflammatory variables shown in the white box are common

manifestations of sepsis that are not linked to any organ damage specifically.


24

Figure 2.7: Physiological changes seen during sepsis according to the 2001 International Sepsis Definitions Conference (Levy et al. 2003). Sepsis patients may present with some or all of these.

Table 2.1: Treat infection variables and their relation to sepsis pathophysiology and sepsis severity. + designates higher values and - designates lower values of the variables.* designates significant predictor (p<0.05)

Infection Variable

(units) Change in the variable for given severity Predictive Ability (AUC)

Mild Moderate Severe Critical Bacteraemia 30-day

Mortality

Temperature (°C) -/+ ++ ++ ++ or -- 0.62* 0.48

Heart rate(beats/min) ++ ++ ++ ++ 0.59* 0.54*

Respiratory rate

(breaths/min) + ++ ++ +++ 0.52 0.63*

Leukocytes

(cells/mm3) + ++ ++ ++ or -- 0.53 0.56*

Creatinine (mg/dl) + + ++ +++ 0.61* 0.59*

Albumin (g/l) - -- --- ---- 0.63* 0.72*

CRP (mg/l) + +++ +++ ++++ 0.63* 0.45

Lactate (mmol/l) -/+ -/+ + ++ 0.67* 0.54

Mental-status -/+ - - --

Blood pressure

(mmHg) -/+ -/+ - --- 0.57* 0.57*


25

Table 2.1 takes a detailed look at a selection of the variables noted in Figure 2.7:

those used in the Sepsis CPN, and their association with sepsis. The choice of

variables was based on availability of measurements/recorded data in available

patient databases as well as expert opinion regarding the variables involved in the

systemic response to infection. For each variable, + and – indicate that higher- or

lower values, respectively, are associated with given sepsis severities. The changes

in each variable given sepsis severity are based on those in the Treat Sepsis CPN.

The predictive ability is measured by the area under the ROC curve (AUC). An AUC

= 0.5 is indicative of no discrimination and AUC = 1 is perfect discrimination. To

compute the AUC, it was assumed that a higher value of the variable would predict

bacteraemia and 30-day mortality, with the exception of albumin and systolic blood

pressure, where the opposite was assumed. The dataset used consists of 3589 patient

cases collected during trials of Treat at Beilinson Hospital, Petah Tiqva, Israel,

between 2004 and 2011. The dataset is described further in Chapter 4.

After identifying candidate model variables, it is necessary to specify the model

structure. The simplest version of a CPN is the so-called “naive Bayes” model, where

all of the effects are directly linked to one cause, as shown in Figure 2.8. However,

“naive Bayes” requires that all of the variables are independent, which is not the case

for many of the sepsis variables. The original constructors of the Sepsis CPN got

around this problem by performing a factor analysis – a dimensional reduction

technique – to group the observable parameters beneath a set of statistically

constructed independent factors (Leibovici et al. 2000). The result was four

intermediate factors that described 80% of the variation in the data. The model

Figure 2.8 ”Naive Bayes” model of a disease

structure is shown in Figure 2.9.It was speculated that these factors may have physical

analogues – when the same method was used on a set of data including inflammatory

mediators, it was found that interleukin 6 (IL-6) had a loading of 0.91 on ‘fever

factor’ – fever factor could be renamed IL-6 and given real units, and tumour necrosis

factor alpha (TNF-α) had a loading of 0.50 on ‘shock factor’ – i.e. it is a major cause

of shock factor (Leibovici et al. 2000). The correlation with real physical parameters

provides further validation of the technique.


26

Figure 2.9: Structure of Treat’s sepsis CPN. Sepsis (red) causes changes in the set of observable parameters (green nodes) through four intermediate factors: ’Fever_factor’, ’Alb_factor’, ’Leuko_factor’ and ’Shock_factor’ (yellow nodes).

2.4.2. DESCRIBING THE PATIENT’S CONDITION

We want to express the severity of a patient’s sepsis on a scale from no sepsis to

critical sepsis. To do this, we need to make a mathematical description of how each

of the infection variables in the Sepsis CPN behave according to the severity of

sepsis. The construction of the CPN model takes therefore a top-down approach,

asking, for example: given that a patient has moderate sepsis, what is their

temperature? The temperature of the ‘patient’ is then expressed as a probability

distribution. This probability distribution may be continuous Gaussian distributions

or discrete distributions, the latter was used in the original Sepsis CPN.

Table 2.1 is constructed from a combination of literature knowledge and expert

opinion. Finding the numbers to complete the construction of the CPN can then be

seen as the conversion of Table 2.1 to a set of conditional probability tables. For

patients with no sepsis, it is assumed that they will fall within the normal range.

The construction of the sepsis CPN is completed by translating the knowledge

contained in Table 2.1 into conditional probability tables. In the original Treat sepsis

network, the factor nodes had three states: no, moderate and severe. Figure 2.10 uses

temperature as an example to show how these distributions look for each state of

sepsis. In addition to the no sepsis group, the former Treat sepsis CPN recognised

four severity groups for bacterial sepsis: mild, moderate, severe and critical. The

green bars and the numbers next to them reflect the probability of a patient having a

temperature in the specified range, given that they have the degree of sepsis

highlighted by the red bar. As expected from Table 2.1, there is little distinction

between the temperature distributions for moderate, severe and critical sepsis, but

they are all significantly different to the no sepsis group.


27

Figure 2.10: Distribution of temperature (fever) for patients with, from left to right, no; moderate; severe; and critical sepsis. The red bars highlight the given severity of sepsis and the green bars represent the respective probability distributions across the temperature groups.

Once the specification of the conditional probability tables is complete, the CPN can

be compiled and used. An example of the CPN in use is shown in Figure 2.11. The

evidence entered into the model is given by the black text below the nodes. The

monitor windows show the inferred probabilities. It is possible to see that each of the

“factor nodes” can be activated differently; in this case “Leuko_factor” has more

severe evidence entered into its children, showing almost 50% probability of the state

“severe”, much higher than that observed for “Alb_factor” and “Fever_factor”. The

children of “Shock” are all set to no or normal, resulting in the probability of “Shock”

less than 0.001%. The combined evidence is used to infer that the patient most likely

has “moderate” sepsis.

Figure 2.11: The Treat sepsis CPN in use. Evidence entered is shown by the text beneath the nodes, and monitor windows are opened to show the inferred probabilities. Figure adapted from (Andreassen et al. 2005).

29

CHAPTER 3. MANUAL LEARNING:

DEVELOPMENT OF CONTINUOUS

DISTRIBUTIONS

This chapter is based on Paper I, entitled “A Bayesian Approach to Model

Development: Design of Continuous Distributions for Infection Variables”. This

paper described the process of updating the Treat Sepsis CPN, subsequently referred

to as the discrete sepsis or D-Sepsis CPN, to the continuous sepsis or C-Sepsis CPN.

This “manual learning” process represents the first stage of the PhD project’s model

development stage, highlighted in Figure 3.1.

Figure 3.1 Sepsis CPN development framework. Dark blue boxes represent the stages of model development for the Sepsis CPN, other boxes represent the inputs to each construction or learning phase. This chapter describes the highlighted section: the development of the C-Sepsis CPN from the D-Sepsis CPN.

The aim of constructing the C-Sepsis CPN was to improve the performance of Treat

and remove some of the undesirable behaviour associated with discrete nodes.

”Jumping” in the assessment of the patient state was one such behaviour: the

discretization of temperature meant that an increase from 38.6 °C to 38.7 °C could

result in a large jump in the assessed illness severity, while an increase from 38.5 °C

to 38.6 °C led to no change.

The distributions for each infection variable were learned manually via a semi-formal

process where the discrete variables in the D-Sepsis CPN were converted to

continuous variables and revised based mainly on expert opinions and the literature.

In the C-Sepsis CPN, each infection variable is described as a normal- or log-normal

distribution for five illness severities termed no, mild, moderate, severe and critical.

A literature search was conducted for each infection variable; some variables were

well reported in the literature as they have been researched as sepsis biomarkers while

others had little literature available. To describe the process of defining continuous


30

variables we looked at two examples, one for which much literature is available, CRP,

and one for which little is available, albumin.

For CRP, the literature search returned 1654 studies, of which 20 were relevant and

of sufficient quality to conduct a meta-analysis. The meta-analysis involved grouping

patients according to the severity of their illness, and the aetiology (infectious/non-

infectious). In all, nine classifications were used: 4 infectious; viral infection, sepsis,

severe sepsis and septic shock, and 5 non-infectious; healthy, no SIRS (patients who

may be ill but do not meet the SIRS criteria), SIRS, severe SIRS and non-septic

shock. A pooled, log-normal distribution was calculated for each of the nine

classifications, the result of which was the 9 distributions shown in Figure 3.2.

Figure 3.2 Log-normal distributions for 4 infectious (top panel) and 5 non-infectious (bottom panel) patient groups. Individual distributions are the result of meta-analysis of literature studies. Figure from Paper I (Ward et al. 2014).

The distributions described in Figure 3.2 were formed based on literature definitions

of sepsis and SIRS patients, and must therefore be mapped to the five illness

severities used in the C-Sepsis CPN. The C-Sepsis CPN distributions shown in Figure

3.3 were defined after input from experts, the details of how this was done are

described in Paper I.

A similar literature search was conducted for albumin, however none of the 244

resulting papers were suitable for defining explicit distributions for albumin stratified

by sepsis severity and/or aetiology. The impossibility of a meta-analysis meant that

sepsis/SIRS severity-based distributions for albumin must be designed in a different

CHAPTER 3. MANUAL LEARNING: DEVELOPMENT OF CONTINUOUS DISTRIBUTIONS

31

Figure 3.3 Transformation of the normal distributions from the meta-analysis (left) to the C-Sepsis distributions (right). Figure from Paper I (Ward et al. 2014).

way. The discrete distributions used in the D-Sepsis CPN were used along with data

from the Treat study (Paul et al. 2006b) to set the range to be covered by the set of

distributions. Literature was available to define a distribution for the ”no” severity;

the distribution was taken from a large study of albumin as a predictor of mortality

(Corti et al. 1994). Albumin is also a concentration-dependent predictor of poor

outcome (Vincent et al. 2003), with low albumin being correlated with high severity.

The distributions implemented in the C-Sepsis CPN are shown in Figure 3.4.

Figure 3.4 C-Sepsis distributions for Albumin. Figure from Paper I (Ward et al. 2014).


32

As a validation step, the predictive abilities of the D-Sepsis and C-Sepsis CPNs were

compared. The Treat CPN, in addition to providing treatment advice, can be used to

make a prediction of the probability of bacteraemia. The data used was collected from

263 patients suspected of infection in the acute ward at Hvidovre Hospital,

Copenhagen University Hospital, Denmark from November 2011 to May 2012. Of

the included patients, 19 (7.2%) had bacteraemia.

The predictive ability of each model (Treat with the D-Sepsis CPN, Treat with the C-

Sepsis CPN) was assessed using the area under the ROC curve (AUC): greater area

under the curve means better predictive ability. The AUC for the C-Sepsis CPN

model was 0.80 (95% Confidence interval (CI) 0.70-0.90) while the AUC for the D-

Sepsis CPN model was 0.73 (95% CI 0.62-0.85). The two curves are shown overlaid

in Figure 3.5. The difference between the two curves was not statistically significant

(p=0.3), however it suggests that the manual construction of continuous nodes in the

Treat sepsis CPN can improve the prediction of bacteraemia. This result provided

motivation for further testing using a larger database, and further development of the

model through the application of automatic learning methods to adjust the prior

probability distributions. In subsequent use of the C-Sepsis model, other issues were

noted such as extremely large odds ratios when approaching the upper- and/or lower

limits of the physiological range for some of the infection variables, notably CRP.

Figure 3.5 ROC curves for bacteraemia prediction for Treat with the D-Sepsis and C-Sepsis CPNs. Figure from Paper I (Ward et al. 2014).

33

CHAPTER 4. AUTOMATIC LEARNING:

MODEL TUNING TO IMPROVE

PREDICTIVE PERFORMANCE

Following the manual learning described in Chapter 3, the C-Sepsis CPN was

transformed into a Learned Sepsis CPN as described by the highlighted section of

the model-development framework in Figure 4.1. This chapter is based on Papers II

and III, which describe the steps taken to tune the C-Sepsis CPN to predict 30-day

mortality, with the results being the L-Sepsis CPN (Paper II) and the LA-Sepsis CPN

(Paper III). Using a similar learning strategy, the C-Sepsis CPN was also tuned to

predict bacteraemia, forming a standalone “SepsisFinder” model.

Figure 4.1 Sepsis CPN development framework. Dark blue boxes represent iterations of the Sepsis CPN, the other boxes represent the inputs to each construction or learning phase. This chapter describes the highlighted section: the development of the L-Sepsis CPN from the C-Sepsis CPN.

The C-Sepsis CPN removed the undesirable behaviours of the D-Sepsis CPN, such

as jumps in the assessment of the patient state in response to small changes in the

input variables. Validation using a small dataset (263 patients) showed a non-

significant improvement over the D-Sepsis CPN for the prediction of bacteraemia.

However, other undesirable behaviours were noticed, such as excessively large odds-

ratios in patients who presented with values of infection variables in ranges that

weren’t suitably covered by the continuous distributions. The aim of automatic

learning was to improve the predictive performance of the network.

The data material used for learning was taken from a set of patient data collected

during trials and/or studies of the Treat system (Andreassen et al. 2005, Paul et al.

2006b) at Beilinson Hospital, Rabin Medical Centre in the period from 2004-2011.

Patients were included in the studies based on suspicion of infection which included

those for whom blood was drawn for culture, those receiving antimicrobials not for


34

prophylaxis, those with SIRS and those with a clinically identified focus of infection

(Paul et al. 2006b). The data included information on infection variables such as the

patients’ vital parameters, clinical chemistry and blood gases, empirically prescribed

treatments, the results of blood and other cultures including in vitro susceptibility

testing, 30-day mortality, and a final clinical diagnosis. The diagnosis allowed

patients to be divided into infectious- and non-infectious groups: data were available

for 3589 patients, of whom 2855 had a confirmed infectious or non-infectious

diagnosis. The infectious diagnoses also allowed sub-groups to be defined for

different sites of infection, for example lower respiratory tract or urinary tract

infections. The remaining 734 patients had an unknown or uncertain final diagnosis.

The EM learning algorithm offered by Hugin was used to learn the LA-Sepsis CPN

(Section 2.2.2). The previous semi-formal “manual” learning process connected

continuous distributions to literature defined sepsis severities: sepsis, severe sepsis

and septic shock, which were then related to our own severity states: no, mild,

moderate, severe and critical. Automatic learning from data allows us to move a step

further away from the literature distributions and relate our sepsis severity states

directly to patient mortality. This represents an important step in the development of

the LA-Sepsis CPN.

Figure 4.2 The LA-Sepsis CPN structure, figure from Paper III. Nodes are represented by ovals, causal links by arrows. Causality is expressed through conditional probability tables. The nodes with double rings represent stochastic variables with continuous probability distributions. The remaining nodes have discrete probability distributions. NSIRS is the non-infectious systemic inflammatory response syndrome. Nodes not learned are shown in blue.

The structure of the LA-Sepsis CPN is shown in Figure 4.2 Three potential causes for

death are given: NSIRS, sepsis and background, where background represents all

other causes. NSIRS and sepsis are assumed to have the same mortality rates for a

given illness severity (Vincent et al. 2006, Dulhunty et al. 2008). Mortality rates are

loosely based on the pneumonia severity index (PSI) (Fine et al. 1997) in combination

with the sepsis literature, where the latter is used to define the mortality rates for

CHAPTER 4. AUTOMATIC LEARNING: MODEL TUNING TO IMPROVE PREDICTIVE PERFORMANCE

35

severe and critical sepsis. The mortality rates used are 0%, 1%, 8%, 45% and 75%

for no, mild, moderate, severe and critical, respectively.

Figure 4.3 An example of initial specified distributions (A) and learned composite distributions (B) for one of the variables in the sepsis CPN: albumin. Each of the distributions in Panel B is a linear combination of the distributions in Panel A. Figure from Paper II (Ward, Andreassen 2015).

Figure 4.3 shows the result of automatic learning for one of the infection variables:

albumin. A set of normal distributions, covering the physiological range observed in

the patient data, was generated for each variable. Panel A shows these distributions

for albumin. Through the EM learning process composite curves are learned for each

severity state by learning the tables for the “factor-mapping” nodes (yellow in Figure

4.2). The resulting curves, shown in Panel B, are linear combinations of the curves

in Panel A. As noted in Chapter 3, albumin is a concentration-dependent predictor of

outcome, which is confirmed here: the more severe states are associated with lower


36

albumin, although the differences between the mild/moderate and severe/critical

distributions are minimal.

Another feature introduced in the C-Sepsis CPN was the possibility to differentiate

between NSIRS and sepsis. During automatic learning, the links between the NSIRS

severities and the four sepsis factors are learned (Figure 4.2: yellow nodes). Each

factor can be considered a branch of the immune system, as suggested by the factors’

correlation with inflammatory mediators (Section 2.4.1). Each branch may be

activated differently according the aetiology of inflammation, i.e. infectious or non-

infectious. Panel A of Figure 4.4 shows the difference in temperature for sepsis =

moderate and NSIRS = moderate. Patients with the infectious aetiology (sepsis)

present with a higher fever than those without infection (NSIRS) for a given severity

of illness. For variables that do not differentiate between infection and no infection,

such as systolic blood pressure (Figure 4.4 Panel B), no such difference is seen.

Figure 4.4 Conditional probability distribution for temperature (panel A) and systolic blood pressure (panel B) for Sepsis and NISIRS patients with severity = moderate. Figure from Paper III.

The area under the ROC curve is used to assess the ability of each model to predict

30-day mortality. Figure 4.5 shows ROC curves for the C-Sepsis, L-Sepsis and LA-

Sepsis CPNs. The AUCs for the C-, L- and LA-Sepsis CPNs were 0.65, 0.74, and 0.79

respectively. Each improvement (C- to L-, L- to LA-) was also statistically significant

(p=10-8, p=0.0004 respectively). To guard against overfitting, cross-validation was

also carried out as part of the development of the L- and LA-Sepsis CPNs, this is

described in further detail in Papers II and III.


37

Figure 4.5 ROC curves for the prediction of 30-day mortality for the C-Sepsis, L-Sepsis and LA-Sepsis CPNs. Figure from Paper III.

In a clinical setting, patients may be graded by a clinical score such as SIRS or

mREMS (modified Rapid Emergency Medicine Score) (Olsson, Terént & Lind 2004,

Howell et al. 2007). Both SIRS and mREMS could be calculated for only 708 patients

(25% of all patients). The 30-day mortality for these patients was 9.9%. Another

score, the MEDS (Mortality in Emergency Department Sepsis) score (Shapiro et al.

2003), could not be calculated given the available patient data. Figure 4.6 shows ROC

curves for the prediction of 30-day mortality for the LA-Sepsis CPN, mREMS and

SIRS scores. The LA-Sepsis CPNs prediction of 30-day mortality outperforms the

SIRS and mREMS scores. The AUC of the LA-Sepsis CPN also compares well with

the reported performance of MEDS, where the AUC ranged from 0.75-0.88

(Carpenter et al. 2009). The low number of patients for whom the clinical scores

could be calculated underlines the advantage offered by CPNs with their ability to

handle missing data.

In addition to the discriminative ability assessed by the ROC curve, calibration is

assessed by the Hosmer-Lemeshow statistic. Figure 4.7 shows the calibration curve

for the LA-Sepsis CPN. Perfect calibration is seen on the curve as a straight y=x line,

i.e. predictions match the observations. A non-significant Hosmer-Lemeshow test

result (p>0.05) signifies that the model is well calibrated. The LA-Sepsis CPN is

therefore a well-calibrated model.


38

Figure 4.6 ROC curves for the prediction of 30-day mortality for the LA-Sepsis CPN, and the SIRS and mREMS scores.

Figure 4.7 Hosmer-Lemeshow calibration curve for the prediction of 30-day mortality using the LA-Sepsis CPN. Figure from Paper III.


39

Despite the model being well-calibrated overall, we noted some differences in

calibration when conducting a sub-group analysis. Figure 4.8 shows regression lines

for patients in the two most prevalent infection sites: lower respiratory tract (LRT)

infections and urinary tract infections (UTI). There were 697 LRT infections with

128 deaths and 486 UTIs with 41 deaths. The gradients of the regression lines in

Figure 4.8 show that for a given severity of the immune response, an LRT infection

is more likely to lead to death. This trend was visible for both the L-Sepsis and LA-

Sepsis CPNs.

Prior to the LA-Sepsis CPN, the Sepsis CPNs were limited to describing the

manifestations of sepsis and NSIRS. Risk factors are commonly included in clinical

scores such as MEDS. The inclusion of age as a risk-factor in the LA-Sepsis CPN

resulted in a significant improvement in the prediction of 30-day mortality compared

to the L-Sepsis CPN. Reintegration within Treat means including a range of other

risk factors, including but not limited to comorbidities and the site of infection. The

difference between UTI and LRT infections shown in Figure 4.8 suggest that

knowledge of the site of infection has the potential to further improve the predictive

performance.

Figure 4.8 Regression lines for the observed 30-day mortality vs. the LA-Sepsis CPN’s predicted 30-day mortality for all 2855 patients (black), 697 patients with a lower respiratory tract infection (red) and 486 patients with a urinary tract infection (green). Figure from Paper III.


40

Using a similar learning strategy, the C-Sepsis CPN was also tuned to predict

bacteraemia, with the result being the “SepsisFinder” model (unpublished). The same

2855 patient cohort was used for the validation of both the LA-Sepsis CPN and

Sepsisfinder. There were 309 patients (10.8%) with bacteraemia. Using SepsisFinder

as a standalone model (not integrated within Treat), the AUC for the prediction of

bacteraemia was 0.74 (95% CI 0.71-0.76). Figure 4.9 shows ROC curves for the 2885

patients from Beilinson Hospital, along with curves for the prediction of bacteraemia

in two cohorts of Danish patients: 263 patients including 19 (7.2%) with bacteraemia

from Hvidovre Hospital (HvH) and 199 patients including 11 (5.5%) with

bacteraemia from Sygehus Lillebælt (SLB). The AUC for SepsisFinder’s prediction

of bacteraemia was 0.74 (95% CI 0.63-0.85) for the HvH patients and 0.79 (95% CI

0.67-0.92) for the SLB patients. SepsisFinder’s stable performance across the three

cohorts suggests that it may not require calibration for local conditions; the response

to sepsis is demographically and geographically invariant.

Figure 4.9 ROC curves for the prediction of bacteraemia using the SepsisFinder model on three cohorts of patients: n=2885 patients from Beilinson Hospital, n=263 patients from Hvidovre Hospital (HvH) and n=199 patients from Sygehus Lillebælt (SLB).

41

CHAPTER 5. APPLICATIONS OF

SEPSISFINDER

This chapter is in part based on Paper IV, which describes one application of the

SepsisFinder model described in Chapter 4: identifying candidates for rapid-

diagnostic testing through risk-based stratification of patients suspected of infection.

This application represents the final stage of the PhD project, an overview of which

is shown in Figure 5.1.

Figure 5.1 PhD project framework. This chapter is associated with the highlighted section: Applications.

Chapter 3 and Chapter 4 described the construction of the C-Sepsis CPN and the L-

and LA-Sepsis CPNs and SepsisFinder, through the manual construction to automatic

learning to tune the CPN. Chapter 4 described tuning the model to predict 30-day

mortality, and the use of the same technique to tune the SepsisFinder model to predict

bacteraemia. The prediction of bacteraemia has significant commercial potential:

rapid diagnostic methods can identify the causative pathogen in sepsis patients much

faster than blood culture, however they are also much more expensive. Identifying a

group of “high-risk” patients where the probability of a positive test is higher has the

potential to increase the cost-effectiveness of these tests. In paper IV, PCR testing

was used as an example to illustrate this principle.


42

We assumed that the added value of a PCR test is defined for the incremental increase

in the number of patients receiving appropriate treatment, due to the identification of

pathogens via PCR. This value is realized as a reduction in mortality: the odds ratio

for 30-day mortality for patients receiving inappropriate empiric treatment against

those receiving appropriate treatment is approximately 1.60 (Paul et al. 2010). We

measure cost-effectiveness relative to standard clinical practice (blood culture alone),

with the costs being the total healthcare costs and the effect being the incremental

reduction in mortality. The cost-effectiveness is assessed by the incremental cost-

effectiveness ratio (ICER) in terms of euros (€) per life-year saved. The ICER is

defined in Equation 5.1. The difference in total healthcare costs, Δcost, is

approximated by the two largest contributors: PCR testing, where nPCR is the number

of tests conducted and costPCR = €300 (Lehmann et al. 2010, Alvarez et al. 2012) is

the cost per test, and the cost of hospitalisation, where nA,add is the additional number

of patients receiving appropriate treatment, ΔLOS is the difference in length of stay

(in days) for patients receiving appropriate and inappropriate treatment and costbed is

the cost of a bed-day. The incremental effectiveness is measured in terms of the

number of life-years saved, where nsurv is the incremental number of survivors and

LYsurv = 5.43 years (Lehmann et al. 2010) is the number of life-years saved per

survivor.

ICER=∆𝑐𝑜𝑠𝑡

∆LY=

𝑛𝑃𝐶𝑅𝑐𝑜𝑠𝑡𝑃𝐶𝑅−𝑛𝐴,𝑎𝑑𝑑∆𝐿𝑂𝑆𝑐𝑜𝑠𝑡𝑏𝑒𝑑

𝑛𝑠𝑢𝑟𝑣𝐿𝑌𝑠𝑢𝑟𝑣 (5.1)

The data material for the assessment was the 3589 patients described in Chapter 4.

Of these patients, 377 had true-positive bacteraemia. True-positive bacteraemia is

defined by positive blood culture of a pathogen determined to be clinically

significant. The significance of the pathogens found by blood culture was assessed

by Treat, Coagulase negative staphylococci, bacillus sp., corynebacteria sp.,

bacteroides sp. and anaerobic gram-positive rods were all considered non-significant

isolates.

The cost-effectiveness analysis used a combination of findings from the dataset along

with figures from the literature, with the two being compared where possible. In

Figure 5.2 the high-risk group was selected as those patients with model predicted

probability of bacteraemia, pBC+, greater than a given threshold PBC+ > 20%. The high-

risk group consisted of n = 700 patients and the fraction of these patients with positive

blood culture, fBC+, was 23.9%. The ICER for the high-risk group was €6,934 (95%

CI €3,669 - €12,484) per life-year and €24,056 (95% CI €15,936 – €38,959) per life-

year for the complementary low-risk group. Confidence intervals were calculated for

a 10,000 trial Monte-Carlo sensitivity analysis wherein all parameters in the cost-

effectiveness model were varied independently according to their underlying

statistical distributions.

CHAPTER 5. APPLICATIONS OF SEPSISFINDER

43

Figure 5.2 Figure from Paper IV. Calculation of the ICER - value is added for the incremental increase in the number of patients receiving appropriate treatment due to the pathogen being identified by PCR

The sensitivity to the model’s selection of a high-risk group was assessed by

repeating the cost-effectiveness analysis for a range of thresholds, PBC+, from 0% to

35% in steps of 2.5%. Table 5.1 presents the median ICER for the low- and high-risk

group for each threshold, PBC+. When the threshold was removed, the ICER was

€16,774 per life-year. The ICER in the high-risk group ranged down to €1,353 per

life-year for PBC+ = 32.5%, while the ICER in the low-risk group reached a maximum

of €534,355 per life-year when PBC+ = 2.5%.


44

Table 5.1: ICERs for complementary low- and high-risk groups for thresholds, PBC+, ranging from 0% to 35% in steps of 2.5%

Threshold,

PBC+ (%)

nlow-risk

(%)

ICERlow-risk

(€/life-year)

nhigh-risk

(%)

ICERhigh-risk

(€/life-year)

0 0 (0.0) - 3589 (100.0) 16774

2.5 736 (20.5) 534355 2853 (79.5) 12606

5.0 1237 (34.5) 158789 2352 (65.5) 10423

7.5 1734 (48.3) 71570 1855 (51.7) 8906

10.0 2081 (58.0) 42017 1508 (42.0) 8553

12.5 2349 (65.5) 32920 1239 (34.5) 7177

15.0 2546 (70.9) 29870 1043 (29.1) 7735

17.5 2723 (75.9) 27768 866 (24.1) 6775

20.0 2889 (80.5) 24056 700 (19.5) 6934

22.5 3074 (85.7) 21367 515 (14.3) 7090

25.0 3309 (92.2) 20845 280 (7.8) 4281

27.5 3471 (96.7) 18815 118 (3.3) 2653

30.0 3541 (98.7) 17528 48 (1.3) 2353

32.5 3582 (99.8) 16924 7 (0.2) 1353

35.0 3589 (100.0) 16774 0 (0.0) -

Figure 5.3 presents the results of the Monte-Carlo analyses for the full range of PBC+.

Panel A shows the results for the high-risk group, and Panel B the results for the

complementary low-risk group. A threshold of PBC+ = 0% meant that all patients were

assigned to the high-risk group and a threshold of PBC+ = 35% meant that all patients

were assigned to the low-risk group. The threshold for cost-effectiveness defined by

the National Institute for Clinical Excellence (NICE) (Appleby, Devlin & Parkin

2007) is £20,000 to £30,000 (about €35,000, shown as a dashed line in both panels).

When looking at the high-risk group alone, cost-effectiveness is demonstrated

(according to NICE) even when the threshold is removed: the ICER for all patients

is €16,774 per life-year which is significantly lower than the cost-effectiveness

threshold of €35,000 per life year. However, this result does not tell the full story. By

removing the threshold we are including a large number of low-risk patients for

testing. We may instead choose our high-risk group by removing those patients for

whom PCR testing is not cost-effective. At a threshold of PBC+ = 10.0%, the patients

(58.0% of all patients) below this threshold have an ICER = €42,017 per life-year

saved. For these patients, PCR testing is not cost-effective. If the high-risk group is

taken as all patients above this threshold, the ICER is €8,553 per life-year.

In addition to the ICER, hospitals must also consider other practical factors when

choosing to run a test. The absolute cost is important along with the throughput of

the laboratories running the test: it may be simply impractical to run PCR tests on

CHAPTER 5. APPLICATIONS OF SEPSISFINDER

45

every patient suspected of infection. So although we have found that it is not cost-

effective to run PCR for patients below a threshold of PBC+ = 10.0%, this threshold

does not necessarily define the choice of “high-risk” patients for whom testing should

be done. If the number of patients being tested is limited by laboratory throughput,

the threshold for “high-risk” will be set higher. Raising the threshold further will have

the dual effect of reducing the number of tests and increasing the incremental benefit

of each test, seen as the ICER falling with increasing threshold.

Figure 5.3 Figure from Paper IV. Boxplot for the Monte-Carlo analysis repeated at cut-offs of PBC+ = 0% to 35% in steps of 2.5%. Panel A shows the results for the high-risk group and Panel B for the low-risk group.

Risk-based stratification can be used to improve the cost-effectiveness of PCR by

removing patients for whom PCR testing is not cost-effective. PCR in an inpatient

population also provides an opportunity to increase appropriate treatment rates in the

highest-risk patients before they are transferred to the ICU, perhaps even preventing

ICU admissions.

47

CHAPTER 6. DISCUSSION

This chapter discusses the significance of the work completed during the PhD project

and offers suggestions for the direction of future work.

6.1. MAIN FINDINGS

Manual learning: Design of continuous distributions for infection variables

Starting with the D-Sepsis CPN that was part of Treat, the first goal of the PhD project

was to introduce continuous distributions for infection variables, forming the C-

Sepsis CPN. This was done manually, combining expert opinion with knowledge

gleaned from the literature, a method that has been proven successful several times

in CPN construction. The C-Sepsis CPN was validated by comparing the predictive

ability of the C-Sepsis and D-Sepsis CPNs with the remainder of the Treat model

being identical. The C-Sepsis CPN had an AUC of 0.80 for the prediction of

bacteraemia and the AUC for the D-Sepsis CPN was 0.73. The C-Sepsis CPN

represented a sizable improvement in predictive performance, although the small data

material meant that the result was not statistically significant. In addition to the

improvement in predictive performance, the introduction of continuous variables

solved the problem of “jumping” seen in the D-Sepsis CPN, where the discretization

of variables meant that, for example, a change in temperature of 0.1°C could result

in a large jump in the assessed illness severity.

Automatic learning: Tuning via automatic learning to improve predictive

performance

Despite its success, manual learning is limited in what can reasonably be achieved.

The availability of data in the literature was sub-optimal for the majority of

parameters. Additionally, the manual construction involved what was effectively

single-variable analysis. Automatic learning provided a structured way to further

improve the model, tuning it to predict clinical outcomes; either diagnostic (presence

of bacteraemia) or prognostic (30-day mortality).

To facilitate machine learning, the C-Sepsis CPN was clipped out of the Treat model,

and tuned as a standalone entity. The C-Sepsis CPN also allows for discrimination

between infectious and non-infectious inflammation: sepsis and NSIRS. The learning

strategy allowed the model to learn the different effects of sepsis and NSIRS on

individual branches of the inflammatory response.

The L-/LA-Sepsis CPNs resulting from automatic learning were validated by testing

their predictive ability for 30-day mortality. The learned CPNs substantially


48

outperformed both SIRS and the mREMS score: the AUC for 30-day mortality was

0.81, 0.67 and 0.54 for the LA-Sepsis CPN, the mREMS score and SIRS, respectively.

The comparison with clinical scores also highlighted one of the advantages of CPN

models – their ability to handle missing data. For the patient group studied, SIRS and

mREMS scores could be calculated for approximately 50% and 25% of the patients,

respectively. Other scores such as SOFA or MEDS could not be calculated for these

patients.

The performance of the LA-Sepsis CPN as a standalone model for mortality

prediction also motivated the tuning of another version of the Sepsis CPN to predict

bacteraemia – SepsisFinder. SepsisFinder’s performance in the prediction of

bacteraemia was stable across patients from both Denmark and Israel, suggesting that

the Sepsis CPNs may not require calibration for local conditions, that is, the sepsis

response is temporally, demographically and geographically invariant. This is

empirical evidence for one of the tenets used in the construction of Treat: that some

parts of the model require calibration, while other parts, including the Sepsis CPN,

do not.

The SepsisFinder and LA-Sepsis CPNs represent a significant step forward from

Treat’s original D-Sepsis CPN. Both models (considered as standalone entities) have

greater predictive performance than the Treat model for bacteraemia- and 30-day

mortality prediction, while using significantly fewer variables. Another advantage of

the SepsisFinder and LA-Sepsis CPNs is the ability to continually adjust and improve

the models as more data becomes available.

Applications: Risk-based stratification of patients to improve cost-effectiveness

of rapid diagnostics

It was assumed that SepsisFinder, a “lightweight” model tuned to predict

bacteraemia, could be used to stratify patients into risk-groups, as has previously been

done using Treat (Paul et al. 2006a). The SepsisFinder model uses up to 12 routinely

collected variables as opposed to over 100 used by Treat. The AUC for the prediction

of bacteraemia using the SepsisFinder model was 0.75, an improvement on the AUC

of 0.70 reported for Treat on a similar cohort (Paul et al. 2006a).

One of the opportunities for utilising such risk assessment is in tailoring the

diagnostic workup of patients suspected of sepsis. Expensive diagnostics can be made

cost-effective by limiting them to patients where 1) they will most likely be able to

influence treatment and 2) the influence on the treatment will give most benefit.

SepsisFinder can improve the cost-effectiveness of expensive rapid diagnostics by

identifying patients for whom testing would not be cost-effective. In a cohort of 3589

patients, SepsisFinder was able to select 58% of patients for whom PCR testing

would not be cost-effective (ICER = €42000 per life-year).

CHAPTER 6. DISCUSSION

49

If the predictive ability could be further improved, such a risk-assessment could even

be able to guide treatment vs. no treatment without performing the expensive test.

Biomarkers such as procalcitonin and CRP have been suggested as useful candidates

for guiding treatment (van der Does et al. 2016). The SepsisFinder model as a whole

outperforms any individual variable, including CRP, allowing us to think of

SepsisFinder as an intelligent biomarker. The addition of procalcitonin or other

biomarkers to SepsisFinder could potentially further improve the cost-effectiveness

of PCR testing.

6.2. FUTURE WORK

The work described in this thesis will be continued as part of an Industrial PostDoc

project; a collaboration between Treat Systems ApS and Aalborg University, partially

funded by Innovationsfonden Danmark. Over a two year period it is expected that the

risk-assessment model of SepsisFinder will be refined and tested clinically, while

development begins on modules aimed at the early recognition of infection and

revision of treatment in patients for whom infections are not microbiologically

documented. In addition to work on the SepsisFinder model, the LA-Sepsis CPN will

be reintegrated within the Treat model.

SepsisFinder: Standalone risk-assessment

The SepsisFinder model, which had greater predictive power than that seen in

published versions of the Treat model, has value as a standalone system. The future

of SepsisFinder is in its use as an “intelligent biomarker”.

The future strategy for the development of SepsisFinder is fundamentally different to

that used in the development of existing clinical scores. Typically, clinical scores

focus on information and measurements that are easily obtained at the bedside.

However, the integration of hospital wide electronic health records and other IT

systems present an opportunity for easy access to a greater amount of information.

Furthermore, it allows the departure from the subjective evaluations often required at

the bedside, moving towards the use of objective, measured data. Throughout the

PostDoc project, Sepsisfinder will be refined and tested clinically, and a laboratory-

variable-only version, SepsisFinderLite will be created.

Risk-assessment software such as SepsisFinder or SepsisFinderLite also has

immediate commercial potential. Reliable, model-based stratification of patients into

risk-groups provides an opportunity to identify target populations to improve cost-

effectiveness. For example, a group of high-risk patients may be eligible for

expensive rapid diagnostic testing in addition to routine blood cultures.


50

Early-Warning and Treatment revision

The models described in this dissertation may also be extended to create a more

complete picture of the response to sepsis by adding a temporal dimension.

The entire time-course of the infection should be considered: until now, point

estimates of the risk of bacteraemia/30-day mortality have been made at the time

when a patients is clinically recognised as having an infection. This use is valuable

in and of itself as an initial triage tool/risk-stratification and impacts decisions on

patient workup/treatment. However, this intelligent biomarker may also be useful

at other time points.

One such use could be as an in-hospital monitoring tool for the early detection of

hospital-acquired infections. The impact of such technology would be significant,

since time is critical in sepsis patients. Early identification of infection has the

potential to reduce the time to diagnosis and appropriate, live-saving treatment.

An intelligent tool for assessing the clinical success or failure of antibiotic treatment

is also needed; the causative pathogen (and hence the susceptibility to antibiotics) is

found in less than half of all patients with an infection. For these patients, there is no

objective measure of whether the treatment is appropriate and it is difficult to justify

treatment escalation or de-escalation. It is hoped that a SepsisFinder module can

provide support for the decision to revise treatment.

Re-integration within Treat

The original goal of tuning the Sepsis CPN was to improve the overall performance

of Treat’s decision support. The improvements seen in the predictive performance of

the standalone versions of the Sepsis CPN provide reason to believe that re-

integration will give an improvement in performance. Additionally, Treat includes

information on the site of infection, which is related to mortality (Chapter 4).

Therefore, it is expected this can further improve performance. However, the re-

integration is not a trivial cut and paste task. Re-integration will involve some degree

of automatic learning in the full Treat CPN. To our knowledge, there is no existing

descriptions of learning in such large CPNs, and computational problems are bound

to arise.

Treat Steward, the software package which includes the Treat CPN, is a fully

integrated system that combines antimicrobial stewardship with advanced decision

support. The purpose of antimicrobial stewardship is to promote the rational use of

antimicrobials, preserving their effectiveness as the prevalence of resistant microbes

increases. It is hoped that the improvements made to Treat Steward’s decision support

through the re-integration of the LA-Sepsis CPN will help in the fight against

antimicrobial resistance.

51

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